Problem: Given $ m \angle LOM = 6x + 148$, and $ m \angle MON = 9x + 2$, find $m\angle MON$. $O$ $L$ $N$ $M$
Answer: From the diagram, we see that together ${\angle LOM}$ and ${\angle MON}$ form ${\angle LON}$ , so $ {m\angle LOM} + {m\angle MON} = {m\angle LON}$ Since $\angle LON$ is a straight angle, we know ${m\angle LON = 180}$ Substitute in the expressions that were given for each measure: $ {6x + 148} + {9x + 2} = {180}$ Combine like terms: $ 15x + 150 = 180$ Subtract $150$ from both sides: $ 15x = 30$ Divide both sides by $15$ to find $x$ $ x = 2$ Substitute $2$ for $x$ in the expression that was given for $m\angle MON$ $ m\angle MON = 9({2}) + 2$ Simplify: $ {m\angle MON = 18 + 2}$ So ${m\angle MON = 20}$.